Answer: Because if he didn't the judges from the allied side would have judged him worthy of death and killed him as they did many of those who ruled Germany during WWII.
He also killed himself for 2 other reasons.
He was in control of the method he would use to kill himself. It is possible that he would choose something a whole lot quicker than (say) hanging.
He would said himself the humiliation of listening what was said about him.
Step-by-step explanation: